Disk drive demodulating a spiral track by finding a maximum correlation between a spiral track crossing signal and a time-shifted nominal spiral track crossing signal

ABSTRACT

A disk drive is disclosed comprising a disk including a plurality of spiral tracks, wherein each spiral track comprises a high frequency signal interrupted by a sync mark at a sync mark interval, and a head actuated over the disk. The spiral tracks are demodulated by reading a spiral track to generate a spiral track crossing signal g(x n ), where x n  is a time in a demodulation window, and determining a position error signal (PES) by determining a time-shift L that maximizes a correlation between g(x n ) and a function that estimates a nominal spiral track crossing signal having the time-shift of L.

BACKGROUND

When manufacturing a disk drive, servo sectors 2 ₀-2 _(N) are written to a disk 4 which define a plurality of radially-spaced, concentric data tracks 6 as shown in the prior art disk format of FIG. 1. Each data track 6 is partitioned into a plurality of data sectors wherein the servo sectors 2 ₀-2 _(N) are considered “embedded” in the data sectors. Each servo sector (e.g., servo sector 2 ₄) comprises a preamble 8 for synchronizing gain control and timing recovery, a sync mark 10 for synchronizing to a data field 12 comprising coarse head positioning information such as a track number, and servo bursts 14 which provide fine head positioning information. The coarse head position information is processed to position a head over a target track during a seek operation, and the servo bursts 14 are processed to maintain the head over a centerline of the target track while writing or reading data during a tracking operation.

In the past, external servo writers have been used to write the product servo sectors 2 ₀-2 _(N) to the disk surface during manufacturing. External servo writers employ extremely accurate head positioning mechanics, such as a laser interferometer, to ensure the product servo sectors 2 ₀-2 _(N) are written at the proper radial location from the outer diameter of the disk to the inner diameter of the disk. However, external servo writers are expensive and require a clean room environment so that a head positioning pin can be inserted into the head disk assembly (HDA) without contaminating the disk. Thus, external servo writers have become an expensive bottleneck in the disk drive manufacturing process.

The prior art has suggested various “self-servo” writing methods wherein the internal electronics of the disk drive are used to write the product servo sectors independent of an external servo writer. For example, U.S. Pat. No. 5,668,679 teaches a disk drive which performs a self-servo writing operation by writing a plurality of spiral tracks to the disk which are then processed to write the product servo sectors along a circular path. Each spiral track is written to the disk as a high frequency signal (with missing bits), wherein the position error signal (PES) for tracking is generated relative to time shifts in the detected location of the spiral tracks. The read signal is rectified and low pass filtered to generate a triangular envelope signal representing a spiral track crossing, wherein the location of the spiral track is detected by detecting a peak in the triangular envelope signal relative to a clock synchronized to the rotation of the disk. However, generating the PES by detecting a peak in a triangular envelope signal representing a spiral track crossing is susceptible to signal noise leading to tracking errors and corresponding errors in the product servo sectors.

There is, therefore, a need to reduce tracking errors when demodulating a spiral track in a disk drive, for example, when servo writing product servo sectors by demodulating prewritten spiral tracks.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a prior art disk format comprising a plurality of concentric data tracks defined by embedded servo sectors.

FIG. 2A shows an external spiral servo writer for writing spiral tracks to the disk according to an embodiment of the present invention.

FIG. 2B shows spiral tracks written to the disk over a partial disk revolution according to an embodiment of the present invention.

FIG. 3 illustrates an embodiment of the present invention wherein each spiral track is written over multiple revolutions of the disk.

FIG. 4A shows an embodiment of the present invention wherein a servo write clock is synchronized by clocking a modulo-N counter relative to when the sync marks in the spiral tracks are detected.

FIG. 4B shows an eye pattern generated by reading the spiral track, including the sync marks in the spiral track.

FIG. 5 illustrates writing of product servo sectors using a servo write clock generated from reading the spiral tracks.

FIG. 6 illustrates an embodiment of the present invention wherein the high frequency signal in the spiral tracks is demodulated by integrating the read signal over a demodulation window and generating the PES relative to a target sync mark and a reference point on the resulting ramp signal.

FIG. 7A shows a nominal spiral track crossing signal according to an embodiment of the present invention.

FIG. 7B shows an embodiment of the present invention wherein a PES is generated relative to a time-shift L that maximizes a correlation between a time-shifted function that estimates the nominal spiral track crossing signal and an actual spiral track crossing signal.

FIGS. 8A-8C illustrate an embodiment of the present invention for generating the function that estimates the nominal spiral track crossing signal.

FIGS. 9A-9C illustrate an embodiment of the present invention wherein a partial spiral track crossing signal may still be demodulated to generate the PES.

FIG. 10 shows an embodiment of the present invention wherein an external product servo writer is used to process the spiral tracks in order to write product servo sectors to the disk.

FIG. 11 shows an embodiment of the present invention wherein an external spiral servo writer is used to write the spiral tracks, and a plurality of external product servo writers write the product servo sectors for the HDAs output by the external spiral servo writer.

FIG. 12 shows an embodiment of the present invention wherein an external spiral servo writer is used to write the spiral tracks, and the control circuitry within each product disk drive is used to write the product servo sectors.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

FIGS. 2A and 2B show a disk drive 16 according to an embodiment of the present invention comprising a disk 18 including a plurality of spiral tracks 20 ₀-20 _(N), wherein each spiral track comprises a high frequency signal 22 interrupted by a sync mark 24 at a sync mark interval (FIG. 4B), and a head 28 actuated over the disk 18. FIG. 7B illustrates how the spiral tracks 20 ₀-20 _(N) are demodulated by reading a spiral track to generate a spiral track crossing signal g(x_(n)), where x_(n) is a time in a demodulation window, and determining a position error signal (PES) by determining a time-shift L that maximizes a correlation between g(x_(n)) and a function that estimates a nominal spiral track crossing signal having the time-shift of L.

The disk drive 16 comprises control circuitry 34 and a head disk assembly (HDA) 32 comprising the disk 18, an actuator arm 26, the head 28 coupled to a distal end of the actuator arm 26, and a voice coil motor 30 for rotating the actuator arm 26 about a pivot to position the head 28 radially over the disk 18. In one embodiment, a write clock is synchronized to the rotation of the disk 18, and the plurality of spiral tracks 20 ₀-20 _(N) are written on the disk 18 at a predetermined circular location determined from the write clock.

The spiral tracks 20 ₀-20 _(N) may be written to the disk 18 using any suitable technique. In the embodiment of FIG. 2A, an entire disk drive 16 is inserted into an external spiral servo writer 36. In an alternative embodiment, only the HDA 32 of the disk drive is inserted into the external spiral servo writer 36. In yet another embodiment, an external media writer is used to write the spiral tracks 20 ₀-20 _(N) to a number of disks 18, and one or more of the disks 18 are then inserted into an HDA 32. In yet another embodiment, the spiral tracks 20 ₀-20 _(N) are stamped onto the disk 18 using magnetic printing techniques.

Referring again to the embodiment of FIG. 2A, the external spiral servo writer 36 comprises a head positioner 38 for actuating a head positioning pin 40 using sensitive positioning circuitry, such as a laser interferometer. While the head positioner 38 moves the head 28 at a predetermined velocity over the stroke of the actuator arm 26, pattern circuitry 42 generates the data sequence written to the disk 18 for a spiral track 20. The external spiral servo writer 36 inserts a clock head 46 into the HDA 32 for writing a clock track 44 (FIG. 2B) at an outer diameter of the disk 18. The clock head 46 then reads the clock track 44 to generate a clock signal 48 processed by timing recovery circuitry 50 to synchronize the write clock 51 for writing the spiral tracks 20 ₀-20 _(N) to the disk 18. The timing recovery circuitry 50 enables the pattern circuitry 42 at the appropriate time relative to the write clock 51 so that the spiral tracks 20 ₀-20 _(N) are written at the appropriate circular location. The timing recovery circuitry 50 also enables the pattern circuitry 42 relative to the write clock 51 to write the sync marks 24 (FIG. 4B) within the spiral tracks 20 ₀-20 _(N) at the same circular location from the outer diameter to the inner diameter of the disk 18. As described below with reference to FIG. 5, the constant interval between sync marks 24 (independent of the radial location of the head 28) enables the servo write clock to maintain synchronization while writing the product servo sectors to the disk.

In the embodiment of FIG. 2B, each spiral track 20; is written over a partial revolution of the disk 18. In an alternative embodiment, each spiral track 20; is written over one or more revolutions of the disk 18. FIG. 3 shows an embodiment wherein each spiral track 20; is written over multiple revolutions of the disk 18.

Referring again to the embodiment of FIG. 2A, after the external spiral servo writer 36 writes the spiral tracks 20 ₀-20 _(N) to the disk 18, the head positioning pin 40 and clock head 46 are removed from the HDA 32 and the product servo sectors are written to the disk 18 during a “fill operation”. In one embodiment, the control circuitry 34 within the disk drive 16 is used to process the spiral tracks 20 ₀-20 _(N) in order to write the product servo sectors to the disk 18. In an alternative embodiment described below with reference to FIGS. 10 and 11, an external product servo writer is used to process the spiral tracks 20 ₀-20 _(N) in order to write the product servo sectors to the disk 18.

FIG. 4B illustrates an “eye” pattern in the read signal that is generated when the head 28 passes over a spiral track 20. The read signal representing the spiral track comprises high frequency transitions 22 interrupted by sync marks 24. When the head 28 moves in the radial direction, the eye pattern will shift (left or right) while the sync marks 24 remain fixed. The shift in the eye pattern (detected from the high frequency signal 22) relative to the sync marks 24 provides the off-track information (position error signal or PES) for servoing the head 28.

FIG. 4A shows an embodiment of the present invention wherein a saw-tooth waveform 52 is generated by clocking a modulo-N counter with the servo write clock, wherein the frequency of the servo write clock is adjusted until the sync marks 24 in the spiral tracks 20 ₀-20 _(N) are detected at a target modulo-N count value. The servo write clock may be generated using any suitable circuitry, such as a phase locked loop (PLL). As each sync mark 24 in the spiral tracks 20 ₀-20 _(N) is detected, the value of the modulo-N counter represents the phase error for adjusting the PLL. In one embodiment, the PLL is updated when any one of the sync marks 24 within the eye pattern is detected. In this manner the multiple sync marks 24 in each eye pattern (each spiral track crossing) provides redundancy so that the PLL is still updated if one or more of the sync marks 24 are missed due to noise in the read signal. Once the sync marks 24 are detected at the target modulo-N counter values, the servo write clock is coarsely locked to the desired frequency for writing the product servo sectors to the disk 18.

The sync marks 24 in the spiral tracks 20 ₀-20 _(N) may comprise any suitable pattern, and in one embodiment, a pattern that is substantially shorter than the sync mark 10 in the conventional product servo sectors 2 of FIG. 1. A shorter sync mark 24 may allow the spiral tracks 20 ₀-20 _(N) to be written to the disk 18 using a steeper slope (by moving the head faster from the outer diameter to the inner diameter of the disk 18), which may reduce the time required to write each spiral track 20 ₀-20 _(N).

In one embodiment, the servo write clock is further synchronized by generating a timing recovery measurement from the high frequency signal 22 between the sync marks 24 in the spiral tracks 20 ₀-20 _(N). Synchronizing the servo write clock to the high frequency signal 22 helps maintain proper radial alignment (phase coherency) of the Gray coded track addresses in the product servo sectors. The timing recovery measurement may be generated in any suitable manner. In one embodiment, the servo write clock is used to sample the high frequency signal 22 and the signal sample values are processed to generate the timing recovery measurement. The timing recovery measurement adjusts the phase of the servo write clock (PLL) so that the high frequency signal 22 is sampled synchronously. In this manner, the sync marks 24 provide a coarse timing recovery measurement and the high frequency signal 22 provides a fine timing recovery measurement for maintaining synchronization of the servo write clock.

FIG. 5 illustrates how the product servo sectors 56 ₀-56 _(N) are written to the disk 18 after synchronizing the servo write clock in response to the high frequency signal 22 and the sync marks 24 in the spiral tracks 20 ₀-20 _(N). In the embodiment of FIG. 5, the dashed lines represent the centerlines of the data tracks. The sync marks in the spiral tracks 20 ₀-20 _(N) are written so that there is a shift of two sync marks 24 in the eye pattern (FIG. 4B) between data tracks. In an alternative embodiment, the sync marks 24 in the spiral tracks 20 ₀-20 _(N) are written so that there is a shift of N sync marks in the eye pattern between data tracks. In the embodiment of FIG. 5, the data tracks are narrower than the spiral tracks 20, however, in an alternative embodiment the data tracks are wider than or proximate the width of the spiral tracks 20.

Once the head 28 is tracking on a servo track, the product servo sectors 56 ₀-56 _(N) are written to the disk using the servo write clock. Write circuitry is enabled when the modulo-N counter reaches a predetermined value, wherein the servo write clock clocks the write circuitry to write the product servo sector 56 to the disk. The spiral tracks 20 ₀-20 _(N) on the disk are processed in an interleaved manner to account for the product servo sectors 56 ₀-56 _(N) overwriting a spiral track. For example, when writing the product servo sectors 56 ₁ to the disk, spiral track 20 ₂ is processed initially to generate the PES tracking error and the timing recovery measurement. When the product servo sectors 56 ₁ begin to overwrite spiral track 20 ₂, spiral track 20 ₃ is processed to generate the PES tracking error and the timing recovery measurement. In the embodiment of FIG. 5, the spiral tracks 20 are written as pairs to facilitate the interleave processing; however, the spiral tracks may be written using any suitable spacing (e.g., equal spacing) while still implementing the interleaving aspect.

FIG. 6 shows an embodiment of the present invention wherein the high frequency signal 22 in a spiral track 20 is demodulated by integrating the read signal to generate a ramp signal 58. The PES is generated relative to a target sync mark 24 in the spiral track 20 and a reference point of the ramp signal 58. In the embodiment of FIG. 6, there are three sync marks 24A-24C in each spiral track crossing (each eye pattern) and the PES is generated as the deviation of the middle sync mark 24B from the center of the ramp signal 58. This deviation can be computed as the difference in the amplitude of the ramp signal 58 when the middle sync mark 24B is detected, or the difference in time between when the middle sync mark 24B is detected and the middle of the ramp signal 58. Also in this embodiment, the demodulation window is opened a number of sync mark intervals preceding the expected spiral track crossing (one sync mark interval in this example) and closed a number of sync mark intervals after the expected spiral track crossing (one sync mark interval in this example). In one embodiment, the ramp signal 58 is generated by integrating the high frequency signal 22 between the sync marks 24; that is, integration windows within the demodulation window are generated corresponding to the segments of high frequency signal 22 between each sync mark 24 (as determined from servo write clock).

Another technique for demodulating the spiral tracks 20 ₀-20 _(N) is illustrated in FIGS. 7A and 7B, wherein FIG. 7A shows a nominal spiral track crossing signal and a function f(x-x₀) that estimates the nominal spiral track crossing signal. During normal operation, when one of the spiral tracks is read to generate a spiral track crossing signal g(x), the PES is generated by finding a time-shift L that maximizes a correlation between the spiral track crossing signal g(x) and the function f(x-x₀) that estimates a nominal spiral track crossing signal having the time-shift of L, where x₀ is a time that corresponds to a peak in the nominal spiral track crossing signal. Any suitable technique may be employed to find the time-shift L that maximizes the correlation, and in the embodiment shown in FIG. 7B, the time-shift L is found that minimizes the mean squared error (MSE) between the actual spiral track crossing signal g(x) and the function f(x-x₀) that estimates a nominal spiral track crossing signal having the time-shift of L.

The nominal spiral track crossing signal of FIG. 7A may be generated using any suitable technique. In one embodiment, the head 28 is servoed over a target radial location of the disk 18 by demodulating the spiral tracks and generating a PES using the integration technique described above with reference to FIG. 6. When the head 28 is positioned directly over the target radial location (PES=0) the sampled spiral track crossing signal g(x_(n)) shown in FIG. 8A is generated, wherein in one embodiment, each sample of the sampled spiral track crossing signal g(x_(n)) is generated by integrating the read signal between the sync marks (sync mark integration window) as shown in FIG. 8A.

In an embodiment shown in FIG. 8B, the nominal spiral track crossing signal is generated by reading a plurality of the spiral tracks. When a particular spiral track crossing signal has a non-zero PES, the resulting read signal samples are shifted by the PES so that the resulting read signal samples align with the PES=0 signal as shown in FIG. 8C. After reading a plurality of the spiral tracks and generating a number of sampled spiral track crossing signals as shown in FIG. 8C, the discrete-time function f(x_(n)-x₀) that estimates the nominal spiral track crossing signal is generated by curve fitting the function to the read signal samples.

In one embodiment, the resolution of the discrete-time function f(x_(n)-x₀) equals the resolution of the PES generated using the function. This is illustrated in FIG. 8C which shows the PES generated relative to:

${S(L)} = {\sum\limits_{n = 1}^{N}\;\left( {{g\left( x_{n} \right)} - {f\left( {x_{n} - x_{0} + L} \right)}} \right)^{2}}$ where x₀ can be any arbitrarily selected offset within the spiral demodulation window.

The PES may then be represented as: PES=L _(min s(L)) +x ₀ In the above equation, N represents the number of samples generated by integrating the sync mark windows for the spiral track crossing signal g(x_(n)). In the example shown in FIG. 8A, there are five samples in the nominal spiral track crossing signal g(x_(n)). The equation S(L) is computed for L=0, L=+1, L=+2, . . . L=−1, L=−2 . . . where the time-shift L is adjusted by a single PES increment. The PES is then selected relative to the time-shift L that minimizes S(L). In an alternative embodiment described below, the above function is evaluated mathematically to derive the time-shift L that results in a minimum (i.e., when the derivative of the above equation equals zero).

Any suitable function f(x_(n)-x₀) for estimating the nominal spiral track crossing signal may be employed in the embodiments of the present invention. The function may be a simple linear function, such as a triangle function, or a more sophisticated function, such as a Gaussian function:

$\frac{1}{\sigma\sqrt{2\pi}}e^{- \frac{{({x_{n} + L})}^{2}}{2\sigma^{2}}}$ In the above equation, the time-shift L is a mean and σ is a standard deviation, where the standard deviation σ is estimated by curve fitting to the read signal samples as illustrated in FIG. 8C.

The logarithm of the above Gaussian function may represented as:

${f(L)} = {{{\ln(A)} - {\frac{\left( {x_{n} + L} \right)^{2}}{2\sigma^{2}}\mspace{14mu}{where}\mspace{14mu} A}} = \frac{1}{\sigma\sqrt{2\pi}}}$ which means the MSE equation can be written as:

${{S(L)} = {{\sum\limits_{n = 1}^{N}\;\left( {{f\left( {x_{n} + L} \right)} - {\ln\left( {g\left( x_{n} \right)} \right)}} \right)^{2}} = {{\sum\limits_{n = 1}^{N}\;\left( {{\ln(A)} - \frac{\left( {x_{n} + L} \right)^{2}}{2\sigma^{2}} - {\ln\left( {g\left( x_{n} \right)} \right)}} \right)^{2}} = \mspace{20mu}{\frac{1}{2\sigma^{2}}{\sum\limits_{n = 1}^{N}\left( {L^{2}\; + {2x_{n}L} + x_{n}^{2} + {2{\sigma^{2}}^{\;}{\ln\left( \frac{g\left( x_{n} \right)}{A} \right)}}} \right)^{2}}}}}}\mspace{14mu}$   Let  a(n) = 2x_(n)   $\mspace{20mu}{{b(n)} = {x_{n}^{2} + {2\sigma^{2}{\ln\left( \frac{g\left( x_{n} \right)}{A} \right)}}}}$ then

$= {\frac{1}{2\sigma^{4}}{\sum\limits_{n = 1}^{N}\;\left( {L^{4}\; + {2{a(n)}L^{3}} + {\left( {{a^{2}(n)} + {2{b(n)}}} \right)L^{2}} + {2{a(n)}{b(n)}L} + {b^{2}(n)}} \right)}}$ $0 = {\quad{\frac{\mathbb{d}{S(L)}}{\mathbb{d}L} = {{{\sum\limits_{n = 1}^{N}\;{4L^{3}}} + {6{a(n)}L^{2}} + {2\left( {{a^{2}(n)} + {2{b(n)}}} \right)L} + {2{a(n)}{b(n)}}} = {{2{NL}^{3}} + {3{\sum\limits_{n = 1}^{N}\;{{a(n)}L^{2}}}} + {\sum\limits_{n = 1}^{N}\;{\left( {{a^{2}(n)} + {2{b(n)}}} \right)L}} + {\sum\limits_{n = 1}^{N}\;{{a(n)}{b(n)}}}}}}}$ By selecting x₀ such that

${\sum\limits_{n = 1}^{N}\;{a(n)}} = 0$ the PES can be determined by finding the time-shift L where:

${{2{NL}^{3}} + {\sum\limits_{n = 1}^{N}\;{\left( {{a^{2}(n)} + {2{b(n)}}} \right)L}} + {\sum\limits_{n = 1}^{N}\;{{a(n)}{b(n)}}}} = 0$ The real root of the above equation represents the time-shift L that minimizes S(L), where the above equation may be solved using any suitable technique, such as a Newton iteration.

Demodulating the spiral tracks by finding the time-shift L that maximizes the correlation between a spiral track crossing signal and a function that estimates a nominal spiral track crossing signal having the time-shift of L improves the signal-to-noise (SNR) and therefore the accuracy in generating the PES. Referring to FIGS. 9A and 9B, if the spiral track crossing signal is shifted so far left or right to be partially outside of the demodulation window, only a partial spiral track crossing signal will be generated. In FIG. 9C, a partial spiral track crossing signal may also be generated due to the product servo sectors 56 overwriting a spiral track as illustrated in FIG. 5. The resulting signal loss may render other demodulation techniques ineffective causing the PES to be discarded which reduces the resolution of the servo system. However, the correlation technique of the present invention improves the PES measurement even for partial spiral track crossing signals such that the PES may still be used by the servo system.

The nominal spiral track crossing signal and corresponding function f(x_(n)-x₀) may be estimated at any suitable location or locations along the radius of the disk. In one embodiment, the nominal spiral track crossing signal and corresponding function f(x_(n)-x₀) are estimated once, for example, near a middle diameter of the disk. In another embodiment, the nominal spiral track crossing signal and corresponding function f(x_(n)-x₀) may be estimated for a number of zones across the disk radius, and in yet another embodiment, the nominal spiral track crossing signal and corresponding function f(x_(n)-x₀) may be estimated for every servo track.

In the embodiment described above with reference to FIG. 5 the spiral tracks are demodulated in order to write product servo sectors 56 ₀-56 _(N) to the disk. During normal operation of the disk drive, the control circuitry 34 demodulates the product servo sectors 56 ₀-56 _(N) to generate the PES used to servo the head during write and read operations. In an alternative embodiment, the control circuitry 34 demodulates the spiral tracks in order to generate the PES for servoing the head during write and read operations. For example, product servo sectors 56 ₀-56 _(N) may be written to the disk by servoing off of the spiral tracks as described above with reference to FIG. 5 except that the servo bursts 14 may be omitted from the product servo sectors. When the control circuitry 34 demodulates the product servo sectors 56 ₀-56 _(N) during normal operation, the residual spiral tracks are also demodulated using the correlation technique in order to generate the fine position information similar to using servo bursts 14.

FIG. 10 shows an embodiment of the present invention wherein after writing the spiral tracks 20 ₀-20 _(N) to the disk 18 (FIGS. 2A-2B), the HDA 32 is inserted into an external product servo writer 60 comprising suitable circuitry for reading and processing the spiral tracks 20 ₀-20 _(N) in order to write the product servo sectors 56 ₀-56 _(N) to the disk 18. The external product servo writer 60 comprises a read/write channel 62 for interfacing with a preamp 64 in the HDA 32. The preamp 64 amplifies a read signal emanating from the head 28 over line 66 to generate an amplified read signal applied to the read/write channel 62 over line 68. The read/write channel 62 comprises circuitry for generating servo burst signals 70 applied to a servo controller 72. The servo controller 72 processes the servo burst signals 70 to generate the PES. The PES is processed to generate a VCM control signal applied to the VCM 30 over line 74 in order to maintain the head 28 along a circular path while writing the product servo sectors 56 ₀-56 _(N). The servo controller 72 also generates a spindle motor control signal applied to a spindle motor 76 over line 78 to maintain the disk 18 at a desired angular velocity. Control circuitry 80 processes information received from the read/write channel 32 over line 82 associated with the spiral tracks 20 ₀-20 _(N) (e.g., timing information) and provides the product servo sector data to the read/write channel 62 at the appropriate time. The product servo sector data is provided to the preamp 64 which modulates a current in the head 28 in order to write the product servo sectors 56 ₀-56 _(N) to the disk 18. The control circuitry 80 also transmits control information over line 84 to the servo controller 72 such as the target servo track to be written. After writing the product servo sectors 56 ₀-56 _(N) to the disk 18, the HDA 32 is removed from the external product servo writer 60 and a printed circuit board assembly (PCBA) comprising the control circuitry 34 (FIG. 2A) is mounted to the HDA 32.

In one embodiment, the external product servo writer 60 of FIG. 10 interfaces with the HDA 32 over the same connections as the control circuitry 34 to minimize the modifications needed to facilitate the external product servo writer 60. The external product servo writer 60 is less expensive than a conventional servo writer because it does not require a clean room or sophisticated head positioning mechanics. In an embodiment shown in FIG. 11, a plurality of external product servo writers 60 ₀-60 _(N) process the HDAs 32 _(i)-32 _(i+N) output by an external spiral servo writer 36 in order to write the product servo sectors less expensively and more efficiently than a conventional servo writer. In an alternative embodiment shown in FIG. 12, an external spiral servo writer 36 is used to write the spiral tracks, and the control circuitry 34 within each product disk drive 16 _(i)-16 _(i+N) is used to write the product servo sectors. 

1. A disk drive comprising: a disk comprising a plurality of spiral tracks, wherein each spiral track comprises a high frequency signal interrupted by a sync mark at a sync mark interval; a head actuated over the disk; and control circuitry operable to demodulate the spiral tracks by: using the head to read a spiral track to generate a spiral track crossing signal g(x_(n)), where x_(n) is a time in a demodulation window; and determining a position error signal (PES) by determining a time-shift L that maximizes a correlation between g(x_(n)) and a function that estimates a nominal spiral track crossing signal having the time-shift of L.
 2. The disk drive as recited in claim 1, wherein the function that estimates the nominal spiral track crossing signal comprises f(x_(n)-x₀) and the control circuitry is further operable to use the equation ${S(L)} = {\sum\limits_{n = 1}^{N}\;\left( {{g\left( x_{n} \right)} - {f\left( {x_{n} - x_{0} + L} \right)}} \right)^{2}}$ to determine the PES.
 3. The disk drive as recited in claim 2, wherein x₀ is a time that corresponds to a peak in the nominal spiral track crossing signal.
 4. The disk drive as recited in claim 1, wherein the control circuitry is further operable to use the PES to maintain the head along a servo track while writing product servo sectors along the servo track.
 5. The disk drive as recited in claim 1, wherein the control circuitry is further operable to generate the spiral track crossing signal g(x_(n)) by integrating a read signal between the sync marks, wherein each sample of the spiral track crossing signal g(x_(n)) represents the integration of the read signal between the sync marks.
 6. The disk drive as recited in claim 1, wherein the control circuitry is further operable to generate the function by reading a plurality of the spiral tracks.
 7. The disk drive as recited in claim 6, wherein the control circuitry is further operable to generate the function by integrating a read signal representing a spiral track crossing to generate an integrated signal, and servoing the head in response to the integrated signal.
 8. The disk drive as recited in claim 6, wherein the control circuitry is further operable to generate the function by sampling a read signal representing a spiral track crossing and curve fitting the function to the read signal samples.
 9. The disk drive as recited in claim 6, wherein the control circuitry is further operable to generate the function by: processing a sampled read signal representing a spiral track crossing to generate a servo signal; servoing the head in response to the servo signal; shifting the read signal samples relative to the servo signal; and curve fitting the function to the shifted read signal samples.
 10. The disk drive as recited in claim 1, wherein the function comprises a Gaussian function.
 11. The disk drive as recited in claim 10, wherein the Gaussian function comprises: $\frac{1}{\sigma\sqrt{2\pi}}e^{\frac{{({x_{n} + L})}^{2}}{2\sigma^{2}}}$ where the time-shift L is a mean and σ is a standard deviation.
 12. A method of operating a disk drive, the disk drive comprising a disk comprising a plurality of spiral tracks, wherein each spiral track comprises a high frequency signal interrupted by a sync mark at a sync mark interval, and a head actuated over the disk, the method comprising: using the head to read a spiral track to generate a spiral track crossing signal g(x_(n)), where x_(n) is a time in a demodulation window; and determining a position error signal (PES) by determining a time-shift L that maximizes a correlation between g(x_(n)) and a function that estimates a nominal spiral track crossing signal having the time-shift of L.
 13. The method as recited in claim 12, wherein the function that estimates the nominal spiral track crossing signal comprises f(x_(n)-x₀) and determining the PES uses the equation ${S(L)} = {\sum\limits_{n = 1}^{N}\;{\left( {{g\left( x_{n} \right)} - {f\left( {x_{n} - x_{0} + L} \right)}} \right)^{2}.}}$
 14. The method as recited in claim 13, wherein x₀ is a time that corresponds to a peak in the nominal spiral track crossing signal.
 15. The method as recited in claim 12, further comprising using the PES to maintain the head along a servo track while writing product servo sectors along the servo track.
 16. The method as recited in claim 12, wherein the spiral track crossing signal g(x_(n)) is generated by integrating a read signal between the sync marks, wherein each sample of the spiral track crossing signal g(x_(n)) represents the integration of the read signal between the sync marks.
 17. The method as recited in claim 12, wherein the function is generated by reading a plurality of the spiral tracks.
 18. The method as recited in claim 17, wherein the function is generated by integrating a read signal representing a spiral track crossing to generate an integrated signal, and servoing the head in response to the integrated signal.
 19. The method as recited in claim 17, wherein the function is further generated by sampling a read signal representing a spiral track crossing and curve fitting the function to the read signal samples.
 20. The method as recited in claim 17, wherein the function is further generated by: processing a sampled read signal representing a spiral track crossing to generate a servo signal; servoing the head in response to the servo signal; shifting the read signal samples relative to the servo signal; and curve fitting the function to the shifted read signal samples.
 21. The method as recited in claim 12, wherein the function comprises a Gaussian function.
 22. The method as recited in claim 21, wherein the Gaussian function comprises: $\frac{1}{\sigma\sqrt{2\pi}}e^{\frac{{({x_{n} + L})}^{2}}{2\sigma^{2}}}$ where the time-shift L is a mean and σ is a standard deviation.
 23. A disk drive comprising: a disk comprising a plurality of spiral tracks, wherein each spiral track comprises a high frequency signal interrupted by a sync mark at a sync mark interval; a head actuated over the disk; and a means for using the head to read a spiral track to generate a spiral track crossing signal g(x_(n)), where x_(n) is a time in a demodulation window; and a means for determining a position error signal (PES) by determining a time-shift L that maximizes a correlation between g(x_(n)) and a function that estimates a nominal spiral track crossing signal having the time-shift of L. 